Triangles

Question 1

What is a triangle?

Answer 1

A triangle is any three sided 2D shape.

Question 2

How can triangles be classified?

Answer 2

According to the length of their sides and according to the size of their angles.

Question 3

How can triangles be classified according to their sides?

Answer 3

Equilateral triangles
Isosceles triangles
Scalene triangles

Question 4

How can triangles be classified according to the size of their angles?

Answer 4

Right angled triangles
Obtuse angled triangles
Acute angled triangles

Question 5

What are the properties of isosceles triangles?

Answer 5

They have two adjacent sides that are equal in length

The angles opposite the sides of equal length are equal

Question 6

What are the properties of a scalene triangle?

Answer 6

They have no sides of equal length

They have no equal angles

Question 7

What are the properties of right angled triangles?

Answer 7

They have one angle that is equal to 90°

A right angled triangle can also be a scalene or isosceles triangle

Question 8

What are the properties of an obtuse angled triangle?

Answer 8

It has one obtuse angle

An obtuse angled triangle can also be an isosceles triangle

Question 9

What are the properties of an acute angled triangle?

Answer 9

It has three acute angles

An acute angled triangle can also be an equilateral triangle

Question 10

What are the properties of equilateral triangles?

Answer 10

They have three sides of equal length
They have three equal angles
Each of the angles is 60°

Question 11

In a triangle, which side is the longest side?

Answer 11

The longest side is always opposite the largest angle.

Question 12

What are the properties of triangles?

Answer 12

They have three sides
They have three angles
If one of the sides of a triangle is produced (extended) then the new angle created on the outside of the triangle is equal to the sum of the two opposite interior angles of the triangle. We call this exterior angles of triangles.
All the angles inside a triangle add up to 180°

Question 12

Where is the perpendicular height found in a right angled triangle?

Answer 12

The perpendicular height is found as a part of the triangle.

Question 13

Where is the perpendicular height found in an acute angled triangle?

Answer 13

It is found inside the triangle.

Question 14

Where is the perpendicular height found in an obtuse angled triangle?

Answer 14

The perpendicular height is found outside of the triangle.

Question 15

What is the Pythagoras theorem?

Answer 15

The theorem states that the hypotenuse squared is equal to the sum of the other two sides squared.

Question 16

What is the hypotenuse?

Answer 16

The hypotenuse is the side opposite the 90° angle.

It is always the longest side.

Question 17

How do we use Pythagoras to work out the base of a right angled triangle?

Answer 17

The hypotenuse squared minus the height squared.

Question 18

How do we use Pythagoras to work out the height of a right angled triangle?

Answer 18

The hypotenuse squared minus the base squared.

Question 19

What are the Pythagoras triplets?

Answer 19

3;4;5
5;12;13
8;15;17
7;24;25

Question 23

What are surds?

Answer 23

Surds are numbers that are left in square root form.

Question 24

How do we simplify surds?

Answer 24

To simplify surds, make the number that is being square rooted a product of its prime factors. Any numbers that are repeated, place their exponential power outside the square root. Any numbers that are not repeated i.e. Not being squared, place inside the square root. If there is more than one number, multiply them together.